Stable manifolds for a class of singular evolution equations and exponential decay of kinetic shocks | Zendy

Alin Pogan | Zendy; Kevin Zumbrun | Zendy

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Stable manifolds for a class of singular evolution equations and exponential decay of kinetic shocks

Author(s) -

Alin Pogan,

Kevin Zumbrun

Publication year - 2018

Publication title -

kinetic and related models

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.987

H-Index - 28

eISSN - 1937-5093

pISSN - 1937-5077

DOI - 10.3934/krm.2019001

Subject(s) - class (philosophy) , boltzmann equation , limiting , exponential function , kinetic energy , shock (circulatory) , mathematics , mathematical analysis , initial value problem , boundary (topology) , cauchy problem , physics , statistical physics , classical mechanics , thermodynamics , computer science , mechanical engineering , medicine , artificial intelligence , engineering

We construct stable manifolds for a class of degenerate evolution equations including the steady Boltzmann equation, establishing in the process exponential decay of associated kinetic shock and boundary layers to their limiting equilibrium states. Our analysis is from a classical dynamical systems point of view, but with a number of interesting modifications to accomodate ill-posedness with respect to the Cauchy problem of the underlying evolution equation.

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